3.1.05

The Butterfly Effect

The "Butterfly Effect", or more technically the "sensitive dependence on initial conditions", is the essence of chaos. This is illustrated in the accompanying applet of the Lorenz Attractor.The "Butterfly Effect" is often ascribed to Lorenz.

In a paper in 1963 given to the New York Academy of Sciences he remarks:

One meteorologist remarked that if the theory were correct, one flap of a seagull's wings would be enough to alter the course of the weather forever.

By the time of his talk at the December 1972 meeting of the American Association for the Advancement of Science in Washington, D.C. the sea gull had evolved into the more poetic butterfly - the title of his talk was* :

Predictability: Does the Flap of a Butterflyâ€™s Wings in Brazil set off a Tornado in Texas?

In the applet we also see a second incarnation of the Butterfly - the amazing geometric structure discovered by Lorenz in his numerical simulations of three very simple equations that now bear his name.